What are the 4 sides?
The semi-circle is one side, then the 2 straight edges, and the arc between them is the 4th side.
That’s what I thought. The only way on which this has four sides is if the semi -circle is a side. But if that’s the case, then I don’t know wha the definition of “side” is
Someone may want to double-check my math on this one, but the length of the sides will be dependant on the radius of the smaller circle
I look at your diagram and see:
ϴ= L/(L+R)
And
2π-ϴ = L/R
I solved those (using substitution, then the quadratic formula) and got
L= π-1 ± √(1+π²) ~= 5.44 or -1.16
Whether or not a negative length is meaningful in this context is an exercise left to the reader
Giving (for L=5.44):
ϴ~= 0.845 ~~48.4°
I’m surprised that it solved to a single number, maybe I made a mistake.
That lines up pretty similarly with what I found also. The angle should be a constant since there is only one angle where the relationship would be true. I just left it in terms of π because I try to avoid rounding.
Having said that, L would be a ratio of r; which I think lines up with what you found as well.
